1. Field of the Invention
This invention relates generally to enhancement of accuracy of sensor devices with known transfer functions and the use of information about the response of a sensor to an input parameter to closely estimate the input parameter, and more particularly concerns a system and method for determining a parameter of breathing gas in a patient ventilator from a sensor for the parameter, based upon a known transfer function of the sensor.
2. Description of Related Art
When a sensor is used to obtain data about a particular characteristic of the environment such as temperature, or the oxygen content of a given gas mixture, for example, the dynamic characteristics of the sensor, as well as the dynamic nature of such a parameter or variable, generally interfere with the accurate assessment of the parameter or variable of interest, unless and until a stable condition of equilibrium is reached by both the parameter or variable of interest to be sensed and the sensor.
The mathematical relationship between the output of a control system and its input is known as the transfer function. For a linear system, the transfer function is the Laplace transform of the output divided by the Laplace transform of the input under conditions of zero initial-energy storage. The dynamic characteristics exhibited by a particular sensor can usually be analyzed and described by the particular transfer function of the sensor. The transfer functions of many sensing elements are already known or easily ascertained, so that the response of the sensor to a given input can readily be determined.
For example, a thermistor typically has a dynamic characteristic such that a period of time elapses following initiation of temperature measurement by the thermistor before the voltage output from the thermistor represents an acceptably accurate reading of the temperature being measured. The graph shown in FIG. 1 illustrates the response of a typical thermistor to a step change in temperature, indicating that at least 0.4 seconds pass before the sensor reading substantially approximates the true value for the temperature.
Similarly, in measurement of flow of a gas with hot film anemometers, knowledge of the temperature of the gas being measured is essential to the estimation of flow. Conventional techniques for measurement of gas flow with hot film anemometers have not been able to eliminate the error introduced by the transient performance of the sensor when the gas temperature changes, and consequently involve waiting until transients in a temperature sensor's output are substantially gone and a steady state has been reached before relying upon a temperature reading. For applications where fast and accurate measurement of the temperature is required, enhancement of the speed and accuracy of an otherwise normally slow and unstable sensor response is desirable.
Other types of sensors also frequently have a time constant (.tau.) for adjustment to a step change of a variable parameter being measured that can be unacceptable where fast and accurate measurements are needed. Typical oxygen sensors, for example, have a time constant in the range of 10 to 15 seconds. Clearly, an oxygen concentration measurement from such a sensor will not be accurate until at least 50 to 75 seconds have elapsed, and then the accuracy typically is not better than 2%. It would be desirable to provide a system and method that allows the use of such otherwise slow sensors to obtain accurate information (accuracy depends on the sensor's estimate of .tau.) about the oxygen content of a gas mixture within a shorter period of time from the onset of the measurement. The present invention meets these needs.